In previous Annual Reports, we described various approaches to summarizing the shape of neuronal dendrites, including a stochastic algorithm with empirical parameters that produces realistic individual dendrites and extensions that compute averages of these. This year we have searched for physiological functions of shape which increase for shapes more closely resembling natural dendrites. If such a function is found, it would suggest a "goal" for the dendrite. We have tried ratios of an estimate of total synaptic input, to dendrite volume used as a measure of metabolic cost. Inputs were weighted by local coupling: the fraction of any injected current that reaches the soma. When input was assumed proportional to coupling-weighted surface area, the access function grew without limit for dendrites with unnatural bulbs at large distances, but not when this was prevented by requiring natural taper, so natural taper was adopted as a constraint. These access functions can grow unnaturally large for large local surface areas, useless for synapses, because they saturate the local extracellular volume. This convinced us to include an explicit estimate of extracellular volume accessed. Local volumes within a distance R of the dendrite were weighted by the electrotonic coupling to the soma of the dendrite nearpoint, and summed. This summed, weighted volume was normalized by dendrite volume. The ratio is greater for branching structures, greater for dendrites which branch more near the soma, a property of motoneurons, and greater when the structures have approximately natural extent. This access function gives a meaning to ideas like "optimum stem diameter" and other natural optimum features. With Dr Smith we have made progress in utilizing "wavelets", an alternative to Fourier transforms, as a mathematical tool to express salient features of cultured neurons and glia.